I'm participating in a free audit of the Baptist Covenant Theology course at the Founders Study Center. In Session 9, Dr. Fred Malone lectures on The Spiritual Nature of the Kingdom of God. Here are my notes from that session (Dr. Malone's explanation supports my understanding of the definition of New Covenant members found in my post here).
Jesus taught that the kingdom of God is a spiritual kingdom. The kingdom of God is made up of those who are born from above by the Holy Spirit. One enters the kingdom of God when the heart has been opened to believe in the Lord Jesus Christ and comes to Him in submission as King. Christians are citizens of the kingdom of God.
Jesus said that (1) His kingdom is not of this world, (2) the kingdom of God has come, (3) the kingdom of God is within you, and (4) the kingdom of God is made up of those who have entered into it by the new birth. It is equivalent to the church invisible; the church made up of the regenerate of all ages.
The kingdom of God forms the local church, but the visible church is not the kingdom of God. The church is only an outpost and a visible manifestation of the kingdom of God.